33 ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , R IO DE JANEIRO 2013
T HE A STROPARTICLE P HYSICS C ONFERENCERigidity Dependence of Forbush Decreases
H.KOJIMA1 , S.S HIBATA2 , A.O SHIMA2 , Y.H AYASHI3 , H.A NTIA4 , S.D UGAD4 , T.F UJII3 , S.K.G UPTA4 , S.K AWAKAMI3 ,M.M INAMINO3 , P.K.M OHANTY4 , I.M ORISHITA5 , T.NAKAMURA6 , T.N ONAKA7 , S.O GIO3 , H.TAKAMARU2 ,H.TANAKA3 , K.TANAKA8 , N.I TO3 , A.JAIN4 , T.M ATSUYAMA3 , B.R AO4 , K.YAMAZAKI3 , N.YOSHIDA2 FOR THE
GRAPES-3 C OLLABORATION .
1 Aichi Institute of Technology
2 Chubu University
3 Osaka City University
4 Tata Institute of Fundamental Research
5 Asahi University
6 Kochi University
8 Hiroshima City University
7 University of Tokyo

shibata@isc.chubu.ac.jp
Abstract: For the study of the propagation and modulations of cosmic rays, it is important to know the mechanismof interactions between primary cosmic rays and the ambient magnetized plasma. As the one of the typicalevents of such interactions, we choose the Forbush decrease in this investigation. To get a clue to figure out themechanism, as the first trial, we have analyzed the relationships between the extent of the dips of cosmic-ray
intensity at Forbush decreases and the rigidity of corresponding primary cosmic rays. For this analysis, we haveused not only the data of a worldwide network of neutron monitors, but also the data obtained using the large areamultidirectional muon telescope of GRAPES-3 at Ooty, India.
Keywords: Forbush decrease, rigidity dependence, Solar flare, propagation and modulations.

1Introduction

For the study of the propagation and modulations of galactic cosmic rays through the Helio magnetosphere, it is important to know the mechanism of interactions between primary cosmic rays and the ambient magnetized plasma.
Forbush decrease is the one of the typical phenomenon ofsuch interactions that the observed intensity of cosmic rays
decreases temporary during magnetic storms. After passing
by the interplanetary shock wave caused by a solar flare
and/or the subsequent Coronal Mass Ejection, the region
where cosmic rays are difficult to penetrate is formed behindthem. In the region, the density of galactic cosmic rays
decreases by more than a few to 10 % at several GV. It iscalled Forbush decrease that the intensity decrease observedat the earth passing through this region. As large Forbush
decreases, 10 to 25 % of decreases have been observed by
the neutron monitor.
Consulting the review of Cane (2000) [1] and following
the preceding studies [2] [3], we decided to analyze the relationships between the extent of the dips of cosmic-ray intensity at Forbush decreases and the rigidity of corresponding
primary cosmic rays, as the first trial, to get a clue to figureout the mechanism of interactions between primary cosmic
rays and the ambient magnetized plasma.

2Rigidity dependence of Forbush decrease

2.1

Observational sites and median rigidities

For this analysis, we have used not only the data of aworldwide network of neutron monitors (NM), but also thedata obtained using the large area multidirectional muon
telescope of GRAPES-3 at Ooty, India. The list of those 17

NM stations and corresponding median primary rigidities(Rm = 10.0 ∼ 31.6 GV) calculated from the tables given byYasue et al. (1892) [4] is shown below (Table.1).
NM station
Alma-Ata
ApatityAthensBeijing
HaleakalaInuvikKeilLomnicky Stit
McMurdoMexicoMoscow
Novosibirsk
Potchefstroom
SouthPole
Tbilisi
Thule
YakutskRm (GV)
15.8
12.6
25.1
25.1
31.6
12.6
15.8
12.6
12.6
25.1
15.8
15.8
20.0
10.0
20.0
12.6
12.6

Table 1: List of NM stations and corresponding medianprimary rigidities (Rm in GV).
For the multidirectional muon telescope of GRAPES-3,
the list of 9 directional components and corresponding median primary rigidities (Rm = 64.4 ∼ 92.0 GV) calculated
by Nonaka (2006) [5] is shown as Table.2.

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33 ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , R IO DE JANEIRO 2013

Rm (GV)
73.2
73.5
92.0
64.4
66.3
82.9
70.0
69.9
88.7

Table 2: List of directional components and corresponding
median primary rigidities (Rm in GV).

2.2

Forbush decrease events

For the present analysis, from the daily averaged data observed by the stations described above [6] during the period
from February 2000 to October 2011, Forbush decrease
events are selected by the following conditions:(1) A candidate of the event is accompanied by a large
solar flare on the list of Space Weather Prediction Center ofNOAA [7](2) For the data of McMurdo station, the event showes
more than 3 % decrease when comparing the average counting rate of three preceding days
28 Forbush decrease events thus selected are listed inTable.3. In the table, sites of the corresponding solar flare
are also listed (9 occurred on the East side and 17 on theWest side). Among them, 26 Forbush decrease events areaccompanied by the solar flares with the X-ray intensity of
M and X classes.
Date2000.02.12
2000.06.09
2000.11.27
2001.04.09
2001.04.12
2001.08.28
2001.09.26
2001.10.22
2001.11.07
2001.11.25
2001.12.31
2002.01.01
2003.05.30
2003.10.22
2003.10.30
2004.11.08
2005.01.03
2005.01.19
2005.07.17
2005.08.25
2005.09.11

Site
E
W
W
E
W
E
E
W
W
W
W
E
W
W
E
W
W
W
E

X-ray (W/m2 )1.3E-05
2.3E-04
4.0E-04
8.4E-05
2.3E-04
5.3E-04
2.6E-04
1.6E-04
1.0E-04
9.9E-05
1.3E-04
5.4E-04
1.7E-032.0E-04
1.7E-04
3.8E-04
1.2E-04
5.6E-05
1.7E-03

Date
2006.12.08
2006.12.15
2011.02.18
2011.02.19
2011.09.11
2011.09.27
2011.10.06

Site
EW
W
WWEW

X-ray (W/m2 )9.0E-04
3.4E-04
2.2E-04
2.2E-04
2.1E-04
1.9E-04
3.9E-05

Table 3: List of Forbush Decreases selected.

3Results and Discussion

For every selected event in Table.3, a scatter plot is drawn
taking the median primary rigidity in the abscissa axis andthe extent of the dip of cosmic ray intensity in the axis ofordinate.
Almost all the scatter plots show very clear median primary rigidity dependence of the dip of a Forbush decrease.
And when they are plotted in log-log scale, almost all theevents show a broken line spectrum as shown in Fig.1, thatconsists of two lines corresponds to the lower rigidities andto the higher ones. This means the data from the muon telescope show the steeper spectrum than those from NM stations. If we calculate the slope (or the power index) for
each line, they show a common tendency of softening.

3.1

Average for the all events

Fig.1 shows the average median primary rigidity dependence of the dip of all 28 Forbush decreases.

1.0
y = -0.6538x + 1.4818
R² = 0.9322

0.8Log(I [%])

Direction
NWNNE
WVE
SWSSE

0.6
y = -1.26x + 2.5034
R² = 0.9782

0.4
0.2
0.0-0.2
1.0

1.2

1.4

1.6

1.8Log(Rm [GV])

2.0

Fig. 1: Median rigidity (Rm in GV) dependence of averageextent (I in %) of the dips for all 28 Forbush decreases
From this average plot (Fig.1), the power indices correspond to each rigidity region are obtained as −0.65±0.05
for the NM stations and as −1.26±0.08 for the muon telescope.

Forbush Decrease
33 ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , R IO DE JANEIRO 2013

1.0

Flare site correspondence

Besides the average feature described in the previous subsection, all the scatter plots indicate some tendency by flare
to flare associated with. That is the flare site effect on theslopes of the rigidity dependence investigated here.
Fig.2 shows the average median primary rigidity dependence of the dip of 9 Forbush decreases associated with thesolar flare on the East side.

1.0
y = -0.7467x + 1.5589
R² = 0.9243

Log(I [%])

0.8

y = -0.6334x + 1.4868
R² = 0.9283

0.8Log(I [%])

3.2

0.6
y = -1.3792x + 2.7464
R² = 0.924

0.4
0.2
0.0

0.6
0.4

y = -1.0939x + 2.1291
R² = 0.979

0.2-0.2
1.0

1.2

1.4

1.6

1.8Log(Rm [GV])

2.0Fig. 3: Median rigidity (Rm in GV) dependence of average
extent (I in %) of the dips for 17 Forbush decreases associated with the solar flare on the West side

0.0
-0.2
1.0

1.2

1.4

1.6

1.8

Log(Rm [GV])

2.0

Fig. 2: Median rigidity (Rm in GV) dependence of average
extent (I in %) of the dips for 9 Forbush decreases associated with the solar flare on the East side
From this average plot (Fig.2), the power indices correspond to each rigidity region are obtained as −0.75±0.06
for the NM stations and as −1.09±0.07 for the muon telescope.
Fig.3 shows the average median primary rigidity dependence of the dip of all 17 Forbush decreases associated withthe solar flare on the West side.
From this average plot (Fig.3), the power indices correspond to each rigidity region are obtained as −0.63±0.05
for the NM stations and as −1.38±0.15 for the muon telescope.
Power indices obtained from these three figures are summarized in Table.4. The corresponding values of determination coefficient (R2 , square of a correlation coefficient) areindicated in the each figure.
Rm in GVSiteAllEastWestNM stations(10.0∼31.6)−0.65±0.05−0.75±0.06−0.63±0.05

muon telescope(64.4∼92.0)−1.26±0.08−1.09±0.07−1.38±0.15

Table 4: Power indices.
Distributions of the power indecies are also shown in
Fig.4 and Fig.fig:muon, for the NM stations and the muon
telescope, respectivery.
From the Table.4 and the distributions (Fig.4 and 5),
power indices for the lower rigidities (NM) become duller

from East to West and power indices for the higher rigidities(muon) steeper from East to West, in an opposite manner.
Though the reason is not clear at this time, we speculatethat the difference possibly reflects the spatial distributionof the diffusion coefficient (or scattering mean free path)of galactic cosmic rays around the magnetically disturbed
region (i.e. the cause for the Forbush decrease) and/or thismight be a hint to theoretical approaches, e.g. Nishida(1983) [8]. The pictures representing our speculation areindicated in Fig.6 and Fig.7, corresponding to East andWest side flare, respectively. For more precise analyses, wemust take into account the effect of detector response to theprimary cosmic rays as Sakakibara et al. (1984) [3].
Acknowledgment:This work is supported by the grants-inaid of the Solar-Terrestrial Environment Laboratory of Nagoya
University and the Institute for Cosmic Ray Research of Universityof Tokyo.

References[1] H.V.Cane, Coronal Mass Ejections and Forbush Decreases,
Space Sci. Revs., 93 (2000) 55-77.
[2] J.A.Lockwood, Forbush Decreases in the Cosmic Radiation,
Space Sci. Revs., 12 (1971) 658-715.
[3] S.Sakakibara, K.Munakata and K.Nagashima, Rigidity
Spectrum of Forbush Decrease, Proc. Int. Sympo. on CosmicRay Modulation in the Heliosphere, Morioka (1984) 212-218
and the references there.
[4] S.Yasue, S.Mori, S.Sakakibara and K.Nagashima, Coupling
Coefficients of Cosmic Ray Daily Variations for Neutron
Monitor Stations, Report of Cosmic-Ray Research Laboratory
No. 7 (1982) Nagoya University.
[5] T.Nonaka, A Study of Loss-Cone Precursor Decrease withGRAPES-3 Muon Telescopes (in Japanese), PhD thethis(2006) Osaka City University.
[6] http://cr0.izmiran.rssi.ru/common/links.htm, Network ofCosmic Ray Stations, RFBR, Russia.
[7] http://www.swpc.noaa.gov/ftpmenu/warehouse.html, Space
Weather Prediction Center, NOAA, USA.
[8] A.Nishida, Numerical Modeling of the Energy Spectrum ofthe Cosmic Ray Forbush Decrease, J. Geophys. Res., 88(1983) 785-791.

Forbush Decrease
33 ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , R IO DE JANEIRO 2013

6neutron E

neutron W

5FlareSunFrequency

4

Shock wave
321

Magnetic Field

0-3.6

-2.8

-2.0

-1.2-0.4

Earth0.4

Power Index

Fig. 4: Power index distribution for the data of the NMstations

Fig. 6: In case of East side flare, the interplanetary magnetic
field near the earth might be more compressed by the shockwave.

6muon Emuon WSun5

FlareFrequency

43

Shock wave

21EarthMagnetic Field

0-3.6-2.8-2.0-1.2

Power Index

-0.4

0.4

Fig. 5: Power index distribution for the data of the muon
telescopeFig. 7: In case of Wast side flare, the interplanetary magnetic
field near the earth might be less compressed by the shockwave.